Can customers create accounts?

Yes they can, through several different methods.

During Checkout

You can enable the registration and login forms on the checkout page. Under Downloads → Settings → Misc site owners have the option of including the login form, the registration form, or both on the checkout page.

When the above option is set to show both the login for and the registration form then checkout will look like the one below. Note the Login link at the top and the registration form at the bottom.

Anywhere On Your Site

If you would like your customers to simply be able to create an account before purchasing or browsing the site you may use the shortcode [edd_register] and it will create a form for registration. See image below. More documentation on [edd_register] here.